Thermodynamics of confined quarks

We investigate the thermodynamics of strongly interacting matter described as a system of quarks and antiquarks in free creating and annihilation, but with pairwise confinement to a volume of hadronix size ($\sim \frac{4\pi }{3{m_{\pi }}^3}$). At low temperature, such a system behaves like a hadron gas, giving a quark or an antiquark a spatial mobility of order ${m_{\pi }}^{-1\mathrm{}}$. At high temperature and hence high density, we obtain a gas of free quarks and antiquarks with infinite spatial mobility. By calculating the crossover of low- and high-temperature approximations, we find a phase transition from hadron to quark matter at the critical temperature $T_c\simeq m_{\pi }$. We compare our results with similar considerations based on the size of hadrons and on perturbative quantum chromodynamics.